Development and Experimental Validation of a Dispersity Model for In Silico RAFT Polymerization

The exploitation of computational techniques to predict the outcome of chemical reactions is becoming commonplace, enabling a reduction in the number of physical experiments required to optimize a reaction. Here, we adapt and combine models for polymerization kinetics and molar mass dispersity as a function of conversion for reversible addition fragmentation chain transfer (RAFT) solution polymerization, including the introduction of a novel expression accounting for termination. A flow reactor operating under isothermal conditions was used to experimentally validate the models for the RAFT polymerization of dimethyl acrylamide with an additional term to accommodate the effect of residence time distribution. Further validation is conducted in a batch reactor, where a previously recorded in situ temperature monitoring provides the ability to model the system under more representative batch conditions, accounting for slow heat transfer and the observed exotherm. The model also shows agreement with several literature examples of the RAFT polymerization of acrylamide and acrylate monomers in batch reactors. In principle, the model not only provides a tool for polymer chemists to estimate ideal conditions for a polymerization, but it can also automatically define the initial parameter space for exploration by computationally controlled reactor platforms provided a reliable estimation of rate constants is available. The model is compiled into an easily accessible application to enable simulation of RAFT polymerization of several monomers.


Dispersity Derivation
Assumptions of the model -Under a quasi-equilibrium state -The equilibria can be described by the partition coefficient -Rate constants are only dependent on temperature following Arrhenius -Chain-length dependent termination is only accounted for in the termination parameter.
-Self-initiation, quenching and the formation/decomposition of intermediate radical adduct is assumed to be fast.
-Solvent effects are only accounted for in the solution propagation rate constant Figure S1. Schematic depiction of combining blend and block theory Firstly, a term to describe the probability of propagation in each RAFT equilibrium cycle is defined as, . the ratio of propagation of active polymer chains to all steps using propagating radicals.
To rewrite as a function of conversion the equation for monomer conversion can be rewritten and rearranged to S 22 Propagating chains terminated in each Δ are discretized into their sub populations. As in controlled polymerizations, chains that are growing can terminate, forming blocks, therefore blend strategy is applied. Figure S2. Contributions of termination and livingness in blend and block theory.
T is the number fraction of dead chains whereas L is the number fraction of Living chains.

B. Term 4 -Quantifying Terminative events
Where the termination fraction, is approximated as the ratio of polymer to CTA multiplied by DP[S 35]  We then simplify the initial rate (at t=0) of radical production by assuming that the rate is also dependent on propagation and termination we can get an approximate value for . By assuming that radicals are produced instantaneously at t=0 and the initial rate of propagating radical production will be approximately the initial rate of polymerization as Tackling the double integral, I. The double integral in S 52 is solved analytically in MATLAB using the symbolic math toolbox to give S 53 which can then be simplified and tidied down to S 54. .
The logarithm can then re-written as a Taylor series as in S 55

Simulated data comparing parameters
Here, we gather rate constants, activation energies, , preexponential factors, A, and efficiency constants from experimental and theoretical literature. and A can be found in the literature for propagation and initiator decomposition which can then be used to calculate and , respectively.
Initiator efficiency, are widely assumed to be between 0.3 and 0.8 for azo initiators, consequently a value of 0.5 has been used. Addition rate constants, was estimated based on https://pubs.acs.org/doi/pdf/10.1021/jp900684t , where it is proposed that the value is around 10 6 orders of magnitude. As widely seen throughout the literature we assume that the basic equilibria seen in the main text lies towards the product such that = 1000 for TTCs.   Here, it is assumed that each degree of polymerization eluted in the GPC experiences its own RTD due to laminar flow. Firstly, each chain in the MWD from batch assuming ideal mixing is multiplied through by the residence time distribution function.